Question

factor the trinomial completely. if the trinomial contains a greatest common factor (other than 1), factor it out first.

\\ -x^2 + 18x - 65 \\

select the correct choice below and, if necessary, fill in the answer box within your choice.

a. \\( -x^2 + 18x - 65 = \\)
b. the polynomial is prime.

Explanation:

⚡ Using what you learned: factoring trinomials

Step 1: Factor out the negative sign

Factor out \( -1 \) to make the leading coefficient positive:

$$ -x^2 + 18x - 65 = -(x^2 - 18x + 65) $$

Step 2: Factor the trinomial

Find two numbers that multiply to \( 65 \) and add to \( -18 \):

$$ (-5) \cdot (-13) = 65 $$

$$ -5 + (-13) = -18 $$

Write the factored form of the trinomial inside the parentheses:

$$ x^2 - 18x + 65 = (x - 5)(x - 13) $$

Step 3: Write the complete factorization

Include the negative sign factored out in Step 1:

$$ -(x - 5)(x - 13) $$

Answer:

A. \( -x^2 + 18x - 65 = -(x - 5)(x - 13) \)